Performance Problem [solved]

My best guess would be the same as Kilishan, perhaps some api call is used in your code to an external source which does not perform very well. Try to identify it and possibly cache the result to limit the rate at which the calls are made to lets say once an hour or so.

Does fetching the pages with a commandline tool like wget or curl result in the same delay? That way you can make sure that apache/php is indeed still busy (or more likely just waiting) instead of some weird javascript related client side issue.

You could try to use apache's mod_status to get an inpression of how many connections apache is currently processing.

Have you looked at tools iotop to see if there are weird activities in disk I/O?

iotop shows no activity. I'm not familiar with mod_status, I'll read about it.